Abstract: To design a high-order accurate shock capturing method for hyperbolic conservation laws,we introduce a new power limiter to obtain a second-order power NND scheme and a third order power WNND scheme based on modification of NND scheme and WNND scheme.By applying the limiter to first-order differences of the candidate stencils,the power NND scheme and the power WNND scheme reduce the smearing near discontinuities.The power NND scheme and the power WNND scheme show less dissipation and less spurious oscillations,and catch the discontinuities more accurately than NND scheme and WNND scheme.The results of power NND scheme are similar to those of WNND scheme,and even better in some examples.The simulation of forced oscillation of the NACA0012 airfoil by power WNND scheme is in good agreement with experiments.

Key words: high order schemes, NND schemes, WNND schemes, power limiter